Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is

$$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Time (sec) } & 0.6 & 1.6 & 2.6 & 10 & \infty \\ \hline \text { Output } & 0.78 & 1.65 & 2.18 & 2.98 & 3 \\ \hline \end{array} $$

The Nyquist plot of a strictly stable $G(s)$ having the numerator polynomial as $(s-3)$ encircles the critical point -1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?

The open-loop transfer function of the system shown in the figure, is

$$ G(s)=\frac{K s(s+2)}{(s+5)(s+7)} $$

For $K \geq 0$, which of the following real axis point(s) is/are on the rool locus?

$$ \text { Let } G(s)=\frac{1}{(s+1)(s+2)} \text {. Then the closed-loop system shown in the figure below, is } $$